The present invention relates to an apparatus for filtering and separating flowing media, especially for salt water conversion and water purification via reverse osmosis and ultra-filtration. The apparatus includes a plurality of circular disk-like filter elements which are connected in series and are stacked against one another. Each filter element comprises a plate-like carrier plate, a dish-like guide plate, and a membrane which is disposed between the carrier plate and the guide plate and is covered with a filter sheet or filtering layer. Wheel-like pressure plates are provided at the ends of the stack of filter elements. These pressure plates clamp together the stack of filter elements with a bolt that passes through the central holes of the filter elements.